What is the solution for (d^2y)/(dx^2)+y=32x^3 ?

The solution for (d^2y)/(dx^2)+y=32x^3 is y=c_{1}cos(x)+c_{2}sin(x)+32x^3-192x

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(d^2y)/(dx^2)+y=32x^3

\frac{d ^{2} y}{d x ^{2}} + y = 32 x^{3}

y = c_{1} cos (x) + c_{2} sin (x) + 32 x^{3} - 192 x

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = 32 x^{3}

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + 32 x^{3} - 192 x

y = c_{1} cos (x) + c_{2} sin (x) + 32 x^{3} - 192 x

y^{^{''}} - 0.16 y = 32 cosh (0.4 x)

y^{^{''}} + 9 y = e^{4 x} + 3 x^{2} - 5

y^{^{''}} + (- 4) y^{^{'}} + 4 y = \frac{2 e ^{2 x}}{x}

y^{^{''}} + 3 y^{^{'}} - 4 y = 6 e^{x}

y^{^{''}} - 2 y^{^{'}} + 2 y = 3 e^{x} sec (x)

What is the solution for (d^2y)/(dx^2)+y=32x^3 ?
The solution for (d^2y)/(dx^2)+y=32x^3 is y=c_{1}cos(x)+c_{2}sin(x)+32x^3-192x